Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #88101⋊C3 |
| Fitting | C8×C13 ⋊ C3×C4 |
| Hall | #88101 ⋊ C3 |
| Hall | C13⋊C3 ⋊ #106 |
| Sylow | C13 ⋊ C3×#106 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
Polycyclic presentation:
2^2,3,2^3,13|a^2=d,b^2=e,e^2=f,b^a=be,e^a=ef,g^a=g^8,g^c=g^3,g^d=g^1250 conjugacy classes — view the full character table.
| maximal subgroup of | #72229115, SD16×AGL(1,𝔽13), #72229208, … |
| maximal normal subgroup of | #72229115, SD16×AGL(1,𝔽13), #72229208, … |
| maximal quotient of | #72259418, C2×#88101⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 285);